Showing papers on "Gravitational field published in 1984"

Does the missing mass problem signal the breakdown of Newtonian gravity

Abstract: We consider a nonrelativistic potential theory for gravity which differs from the Newtonian theory. The theory is built on the basic assumptions of the modified dynamics, which were shown earlier to reproduce dynamical properties of galaxies and galaxy aggregates without having to assume the existence of hidden mass. The theory involves a modification of the Poisson equation and can be derived from a Lagrangian. The total momentum, angular momentum, and (properly defined) energy of an isolated system are conserved. The center-of-mass acceleration of an arbitrary bound system in a constant external gravitational field is independent of any property of the system. In other words, all isolated objects fall in exactly the same way in a constant external gravitational field (the weak equivalence principle is satisfied). However, the internal dynamics of a system in a constant external field is different from that of the same system in the absence of the external field, in violation of the strong principle of equivalence. These two results are consistent with the phenomenological requirements of the modified dynamics. We sketch a toy relativistic theory which has a nonrelativistic limit satisfying the requirements of the modified dynamics.

A Study of Terrain Reductions, Density Anomalies and Geophysical Inversion Methods in Gravity Field Modelling

Abstract: : The general principles of the use of known density anomalies for gravity field modelling are reviewed with special emphasis on local applications and utilization of high degree and order spherical harmonic reference fields The natural extension to include also unknown density anomalies will be studied within the framework of geophysical inversion methods, and the prospects for hybrid gravity field modelling/inversion methods will be outlined A very simple case of such methods is the determination of representative topographic densities through collocation with parameters

Gravitationally repulsive domain wall

Abstract: The Gauss-Codazzi formalism is used to obtain exact solutions to Einstein's equations in the presence of domain walls. Domain walls are shown to have repulsive gravitational fields. The most general solution to Einstein's equations for a planar domain wall is obtained. Also, the motion of a spherical domain wall in an asymptotically flat space-time is derived.

Einstein's theory in a three-dimensional space-time

Abstract: As a preparation for studying quantum models, we analyze unusual features of Einstein's theory of gravitation in a three-dimensional space-time. In three dimensions, matter curves space-time only locally and the gravitational field has no dynamical degrees of freedom. The standard correspondence of Einstein's theory with Newton's theory breaks down. A dust distribution moves without any geodesic deviation between the particles. The cosmological models and relativistic stars behave in a qualitatively different way from their Newtonian counterparts. These features are important for the correct understanding of mini-superspace models.

A numerical study of nonspherical black hole accretion. I: Equations and test problems

Abstract: We have developed a 2D axisymmetric, general relativistic code to study inviscid hydrodynamic accretion flows in a fixed Kerr black hole gravitational field. In this first of several papers documenting our methods and results, we describe and discuss the hydrodynamic equations in the form used in the code. Certain analytic solutions for shock tubes and special accretion flows are derived; these solution will form the basis for code testing and calibration.

Relativity and Engineering

Abstract: 1. Kinematics in Inertial Axes.- 1.1 The "Aether" in the Nineteenth Century.- 1.2 Some Experimental Evidence.- 1.3 Einstein's Relativity Postulates.- 1.4 Time and Length Standards. Synchronization.- 1.5 The "Simple" Lorentz Transformation.- 1.6 More General Lorentz Transformations.- 1.7 Time Dilatation and Proper Time.- 1.8 Length Measurements.- 1.9 Volume and Surface Elements.- 1.10 Visual Perception of Objects in Motion.- 1.11 Transformation of Velocities and Accelerations.- 1.12 Four-Vectors.- 1.13 Kinematics in Four Dimensions.- Problems.- 2. Dynamics in Inertial Axes.- 2.1 Equation of Motion of a Point Mass.- 2.2 Mass and Energy.- 2.3 A Few Simple Trajectories.- 2.4 Transformation Equations for Force, Energy, and Momentum.- 2.5 Four-Dimensional Dynamics.- 2.6 Systems of Points.- 2.7 Elastic Collisions.- 2.8 Motion of a Point with Variable Rest Mass.- 2.9 Rocket Acceleration.- 2.10 Inelastic Collisions.- 2.11 Incoherent Matter.- 2.12 The Kinetic Energy-Momentum Tensor.- 2.13 The Total Energy-Momentum Tensor.- Problems.- 3. Vacuum Electrodynamics in Inertial Axes.- 3.1 Transformation Formulas for the Sources.- 3.2 Transformation Equations for the Fields.- 3.3 Force on a Charged Particle.- 3.4 Four-Currents.- 3.5 The Electromagnetic Tensors.- 3.6 Potentials.- 3.7 Transformation of a Plane Wave: The Doppler Effect.- 3.8 The Lienard-Wiechert Fields.- 3.9 Fields of a Charge in Uniform Motion.- 3.10 Fields of a Static Dipole in Uniform Motion.- 3.11 Radiation from an Antenna in Uniform Motion.- 3.12 Radiation from a Moving Oscillation Dipole.- 3.13 Doppler Spectrum from a Moving Source.- Problems.- 4. Fields in Media in Uniform Translation.- 4.1 Polarization Densities.- 4.2 Constitutive Equations.- 4.3 Some Useful Forms of Maxwell's Equations.- 4.4 Point Charge Moving Uniformly in a Dielectric Medium.- 4.5 The Cerenkov Effect.- 4.6 Waves in a Moving Dielectric. The Fresnel Dragging Coefficient.- 4.7 Green's Dyadic for a Moving Dielectric.- 4.8 Electric Dipole Radiating in a Moving Dielectric.- Problems.- 5. Boundary-Value Problems for Media in Uniform Translation.- 5.1 Boundary Conditions.- 5.2 Dielectric Slab Moving in Time-Independent Fields.- 5.3 The Wilsons' Experiment.- 5.4 Sliding Contacts. A Simple Problem.- 5.5 Material Bodies Moving at Low Velocities.- 5.6 Conductors Moving in a Pre-Existing Static Magnetic Field.- 5.7 Circuit Equations.- 5.8 Motional E.M.F..- 5.9 Normal Incidence of a Time-Harmonic Plane Wave on a Moving Mirror.- 5.10 Arbitrary Time-Dependence of the Incident Plane Wave.- 5.11 Oblique Incidence of a Time-Harmonic Plane Wave on a Moving Mirror.- 5.12 A Time-Harmonic Plane Wave Incident on a Dielectric Medium.- 5.13 Reflection of a Plane Wave on a Moving Medium of Finite Conductivity.- 5.14 Revisiting the Boundary Conditions at a Moving Interface.- 5.15 Scattering by a Cylinder Moving Longitudinally.- 5.16 Scattering by a Cylinder Moving Transversely.- 5.17 Three-Dimensional Scattering by Moving Bodies.- 5.18 The Quasistationary Method.- Problems.- 6. Electromagnetic Forces and Energy.- 6.1 Surface and Volume Forces in Vacuum.- 6.2 Maxwell's Stress Tensor.- 6.3 A Few Simple Force Calculations.- 6.4 Radiation Pressure on a Moving Mirror.- 6.5 Radiation Force on a Dielectric Cylinder.- 6.6 Static Electric Force on a Dielectric Body.- 6.7 Magnetic Levitation.- 6.8 Levitation on a Line Current.- 6.9 Electromagnetic Energy in an Inertial System.- 6.10 Four-Dimensional Formulation in Vacuum.- 6.11 The Electromagnetic Energy-Momentum Tensor in Material Media.- Problems.- 7. Accelerated Systems of Reference.- 7.1 Coordinate Transformations.- 7.2 The Metric Tensor.- 7.3 Examples of Transformations.- 7.4 Coordinates and Measurements.- 7.5 Time and Length.- 7.6 Four-Vectors and Tensors.- 7.7 Three-Vectors.- 7.8 Velocities and Volume Densities.- 7.9 Covariant Derivative.- Problems.- 8. Gravitation.- 8.1 Inertial and Gravitational Masses.- 8.2 The Principle of Equivalence.- 8.3 Curvature.- 8.4 Einstein's Equations.- 8.5 The Small-Field Approximation.- 8.6 Gravitational Frequency Shift.- 8.7 Time Measurement Problems.- 8.8 Some Important Solutions of Einstein's Equations.- 8.9 Point Dynamics.- 8.10 Motion in the Schwarzschild Metric.- 8.11 Motion of a Photon in the Schwarzschild Metric.- 8.12 Strongly Concentrated Masses.- 8.13 Static Cosmological Metrics.- 8.14 Nonstatic Cosmological Metrics.- 8.15 Recent Cosmological Observations.- Problems.- 9. Maxwell's Equations in a Gravitational Field.- 9.1 Field Tensors and Maxwell's Equations.- 9.2 Maxwell's Equations in Rotating Coordinates.- 9.3 Transformation Equations for Fields and Sources.- 9.4 Constitutive Equations in Vacuum.- 9.5 Constitutive Equations in a Time-Orthogonal Metric.- 9.6 Constitutive Equations in Material Media.- 9.7 The Co-Moving Frame Assumption.- 9.8 Boundary Conditions.- Problems.- 10. Electromagnetism of Accelerated Bodies.- 10.1 Conducting Body of Revolution Rotating in a Static Magnetic Field.- 10.2 Conducting Sphere Rotating in a Uniform Magnetic Field.- 10.3 Motional E.M.F.- 10.4 Generators with Contact Electrodes.- 10.5 Dielectric Body of Revolution Rotating in a Static Field.- 10.6 Rotating Permanent Magnets.- 10.7 Scattering by a Rotating Circular Dielectric Cylinder.- 10.8 Scattering by a Rotating Circular Conducting Cylinder.- 10.9 Scattering by a Rotating Dielectric Body of Revolution.- 10.10 Scattering by a Rotating Sphere.- 10.11 Reflection from a Mirror in Arbitrary Linear Motion.- 10.12 Reflection from an Oscillating Mirror, at Normal Incidence.- 10.13 Reflection from an Oscillating Mirror, at Oblique Incidence.- 10.14 Scattering by Other Moving Surfaces.- Problems.- 11. Field Problems in a Gravitational Field.- 11.1 Fields Associated with Rotating Charges.- 11.2 Schiff's Paradox.- 11.3 Kennard's Experiment.- 11.4 Optical Rotation Sensors.- 11.5 Scattering by a Rotating Body of Arbitrary Shape.- 11.6 Transformation of an Incident Wave to Rotating Coordinates.- 11.7 Scattered Field in Rotating Coordinates.- 11.8 Two Examples.- 11.9 Low Frequency Scattering by Rotating Cylinders.- 11.10 Quasistationary and Relativistic Fields.- 11.11 Axes in Hyperbolic Motion.- 11.12 The Induction Law.- 11.13 Maxwell's Equations in a Schwarzschild Metric.- 11.14 Light Deflection in a Gravitational Field.- Problems.- Appendix A. Complements of Kinematics and Dynamics.- A.1 Transformation Matrix for the "Parallel" Transformation.- A.2 Transformation with Rotation.- A.3 Transformation of Velocities.- A.4 Relationship Between Force and Acceleration.- A.5 Equations of Motion in Cylindrical Coordinates (r,?,z).- A.6 Equations of Motion in Spherical Coordinates (R,?,?).- Appendix B. Dyadics.- B.1 The Dyadic Notation.- B.2 Operators on Dyadics.- B.3 Green's Dyadic.- Appendix C. Basis Vectors.- Appendix D. Moving Open Circuits.- List of Symbols.- Some Useful Numerical Constants.- References.

Exact theory of the (Einstein) gravitational field in an arbitrary background space-time

Abstract: The Lagrangian based theory of the gravitational field and its sources at the arbitrary background space-time is developed The equations of motion and the energy-momentum tensor of the gravitational field are derived by applying the variational principle The gauge symmetries of the theory and the associated conservation laws are investigated Some properties of the energymomentum tensor of the gravitational field are described in detail and the examples of its application are given The desire to have the total energymomentum tensor as a source for the linear part of the gravitational field leads to the universal coupling of gravity with other fields (as well as to the self-interaction) and finally to the Einstein theory

Renormalization Group Analysis of Grand Unified Theories in Curved Space-time

Abstract: We consider a class of grand unified theories (GUT's) based on the Georgi-Glashow model in curved spacetime. We are particularly concerned with the coupling constants involving the curvature. These include the cosmological and gravitational constants, as well as coupling constants appearing in terms quadratic in the curvature and in terms which link the Higgs bosons to the scalar curvature. For asymptotically free theories, we use the renormalization group to obtain expressions for these effective coupling constants at high curvature (between the GUT and Planck scales). We discuss the role of the effective coupling constants in the gravitational field equations. These results may be of importance for cosmology.

Theory of non-propagating surface-wave solitons

Abstract: An incompressible inviscid fluid contained in a channel in a gravitational field admits soliton-like disturbances where the velocity potential depends upon all three coordinates as well as time, yet its centre of mass can be at rest. These solitons were recently discovered by Wu, Keolian & Rudnick. The calculations are carried out with the multiple-scales approach. Consequences of mass conservation and radiation are discussed.

Re-entry vehicle dynamics

Abstract: Re-entry vehicle dynamics , Re-entry vehicle dynamics , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

Renormalization-group equations in curved space-time

Abstract: This paper presents renormalization-group equations which are given a general formulation in curved space-time. The general form of the equation for the effective charge corresponding to the parameter of nonminimal coupling of a scalar field and the gravitational field is established in the one-loop approximation. It is shown that in the limit of a strong gravitational field the asymptotically free theories can be asymptotically conformally invariant.

Theories of gravitation with nonminimal coupling of matter and the gravitational field

Abstract: The foundations of a theory of nonminimal coupling of matter and the gravitational field in the framework of Riemannian (or Riemann-Cartan) geometry are presented. In the absence of matter, the Einstein vacuum field equations hold. In order to allow for a Newtonian limit, the theory contains a new parameter l0 of dimension length. For systems with finite total mass, l0 is set equal to the Schwarzschild radius.

About an unsuspected integrable problem

Abstract: The motion of a particle orbiting a planet is investigated when both the gravitational attraction of the planet and the radial radiation force due to the Sun are taken into account. Because of this latter force, we introduce a rotating frame so as to maintain the Sun at fixed coordinates.

Mining the Universe

Abstract: The Unruh-Wald scenario for mining quantum black holes is applied to de Sitter space. The following questions are addressed: Will the generalized second law of thermodynamics be maintained for de Sitter horizons. Does the mining process allow the recovery of unlimited energy from the cosmological gravitational field. The evaporation of a black hole in de Sitter space is also investigated in the context of the second law.

Relativistic perturbations of an earth satellite

Abstract: The inertial frame of reference in the neighborhood of a test body provided by the construction of Fermi normal coordinates is generalized to include the effect of the body's gravitational field. The metric obtained provides a simple physical description of relativistic corrections to the orbital motion of a satellite of the Earth. The main correction is the nonlinear Schwarzschild field of the Earth; in these coordinates there are also three much smaller terms arising from the solar tidal influence.

Derivation of the blackbody radiation spectrum from the equivalence principle in classical physics with classical electromagnetic zero-point radiation

Abstract: A derivation of Planck's spectrum including zero-point radiation is given within classical physics from recent results involving the thermal effects of acceleration through classical electromagnetic zero-point radiation. A harmonic electric-dipole oscillator undergoing a uniform acceleration $\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}$ through classical electromagnetic zero-point radiation responds as would the same oscillator in an inertial frame when not in zero-point radiation but in a different spectrum of random classical radiation. Since the equivalence principle tells us that the oscillator supported in a gravitational field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{g}}=\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}$ will respond in the same way, we see that in a gravitational field we can construct a perpetual-motion machine based on this different spectrum unless the different spectrum corresponds to that of thermal equilibrium at a finite temperature. Therefore, assuming the absence of perpetual-motion machines of the first kind in a gravitational field, we conclude that the response of an oscillator accelerating through classical zero-point radiation must be that of a thermal system. This then determines the blackbody radiation spectrum in an inertial frame which turns out to be exactly Planck's spectrum including zero-point radiation.

Hamiltonian formulation of gravitating perfect fluids and the Newtonian limit

Abstract: The canonical formalism is applied to self‐gravitating perfect fluids with particular emphasis on recovering the correct nonrelativistic limit also in (quasi‐) Hamiltonian form. We use essentially Lagrangian coordinates by considering the fluid defined by a map from space‐time into a three‐dimensional material manifold which is equipped with a volume element representing physically the matter (baryon number) density. By eliminating the coordinate freedom in this material space the usual matter conservation and (relativistic) Euler equations are recovered in a (3+1)‐dimensional formalism which makes it very easy to compare them to their nonrelativistic limits. By splitting the 3‐metric and its canonical momenta into a conformal part and the determinant we arrive at a system of evolution and constraint equations for the gravitational field that also has a well‐defined Newtonian limit provided the geometric version of the Newtonian theory is also cast into an analogous (3+1)‐dimensional form. Some of the evolution equations of the relativistic theory, however, become additional constraints in the limit which represents the freezing of the gravitational (or radiation) degrees of freedom. We then use this formalism to rederive the first‐order post‐Newtonian approximation and obtain the standard results in a flexible geometrical form since no gauge or coordinate conditions need be imposed in advance.

Unification of generalized electromagnetic and gravitational fields

Abstract: Structural symmetry between generalized gravitational field (gravito‐Heavisidian field) and the generalized electromagnetic field associated with dyons has been demonsttrated, and the field equations, equation of motion, and the quantization condition for angular momentum operators for both these fields have been unified.

Superfluid He 4 analog of the rf superconducting quantum interference device and the detection of inertial and gravitational fields

Abstract: Superfluid $^{4}\mathrm{He}$ filling a thin torus, interrupted by $N$ weak links in series, is found to give an angular momentum contribution which depends parametrically on the steady absolute rotation of the torus. This in principle enables one to determine off-diagonal components of the local metric. Recent claims for a surprisingly high sensitivity of a similar system to gravitational waves and Lense-Thirring fields are unfortunately ill founded.

The gravitational contribution to the stress-energy tensor of a medium in general relativity

Abstract: The macroscopic stress-energy tensor of an astronomical “medium” such as a galaxy of stars is determined by the field equation of general relativity from the small-scale variations in mass and velocity. In the weak-field, slow-motion approximation, in which the gravitational fields of the stars are Newtonian, it is found that the contribution by the small-scale gravitational fields to the macroscopic density and stress are, respectively, the Newtonian gravitational energy density and the Newtonian gravitational stress tensor. This result is based on the general-relativity field equation, not conservation laws, although the general-relativity field equation has the well-known property of being consistent with conservation laws.

The thermodynamics of gravitational radiation

Abstract: I conjecture, and show for a large class of cases, that given a spacelike hypersurface on which is an arbitrary distribution of linearized gravitons and matter, the latter satisfying the positive energy condition, the expectation value of the number of events in which a graviton is absorbed by or scattered inelastically from the matter within any future time,t, is always less then the expectation value of the number of gravitons in the initial state (except for a set of initial configurations of measure zero). Consequences of this result are: (1) the impossibility of any system containing gravitational radiation reaching thermal equilibrium in a finite time, (2) the absence of an ultraviolet catastrophe for gravitational radiation, (3) the impossibility of measuring accurately the quantum state of the linearized gravitational field, and (4) the impossibility of constructing a gravitational wave laser.

Relativistic deflection of radio signals in the solar gravitational field measured with VLBI

Abstract: For an observer on Earth the general theory of relativity (GR) predicts an apparent outward displacement of a star seen at the Sun's limb of 1.75 arc s. A generalized formulation for gravitational deflection of light1 includes a parameter γ which ranges from 1 (GR) to −1 (no deflection). Early total eclipse measurements2 constrained γ by 20–40%, permitting alternative gravitational theories (for example, ref. 3). Radio interferometer measurements of deflections of extragalactic objects4,5 and timing measurements of spacecraft signals6 have all been consistent with GR with increasing accuracy. We now report the most sensitive measurement of deflection so far achieved, in which very long baseline interferometry (VLBI) observations yield a value of γ of 1.008 with a 1 σ formal standard error of ±0.005.